Yes, agreed.. excellent answers above.
(read this when you get bored
)
And from another angle: The term "biological filter" or "biofilter" for short, refers to one of the three main functions of the physical filter you will buy and use. One function, that of "mechanical filtration" is the one that most people are familiar with, that of trapping particles of debris and waste in the mesh of the sponges or floss in the filter. Another function, that of "chemical filtration" is a special case that we don't usually need under normal circumstances - a common example of that is the use of carbon (aka charcoal, aka activated carbon) which is used to clear medications that have been used or to remove yellow tannins from bogwood or unusual organic smells. Carbon only lasts about 3 days and then can be removed.
The third and, as we've all agreed, most important filter function is that of the biofilter as described by honeythorn and oldman47 up above. I know I'm repeating the pinned articles you've probably read at the top of our forum but its so fascinating: Unlike the carbon dioxide we breathe out, the fish give off ammonia(NH3) when they respire with their gills. Their waste is also broken down into ammonia. The excess food they don't eat and the dead pieces of plants also both break down into ammonia.
Ammonia is bad for fish because is burns their gills. The burning is serious and can cause permanent damage. Amounts even smaller than our test kits can measure cause irritation.
The first of the two good bacteria species that grow in the biofilms on our filter media are the ammonia oxidizers (sometimes we call them "A-bacs" or "AOBs") and they eat ammonia and convert it to nitrite (NO2). A mature A-bac colony is very, very fast at converting ammonia into nitrite.
Nitrites (NO2) are also bad for fish. Nitrite attaches to the hemoglobin molecule in the fishes blood as if it were oxygen. When it does that, it keeps oxygen from being there and the fish begins to suffocate. Even small amounts of this can cause permanent damage.
The second of the two good bacteria, the "nitrite oxidizers" (aka "N-bacs" or "NOBs") will eat nitrite (NO2) and convert it to nitrate (NO3), which is also not a great thing to have in our tanks but it is much, much less toxic to the fish than either the ammonia or the nitrite. Many aquarists like to try and keep nitrates at 40ppm or below as good practice but fish have been found to tolerate quite high amounts, like 100ppm without death. Nitrates get removed by water changes.
Anyway, that's the somewhat longer version that contains what a "biofilter" is, if it was clear enough to follow.
~~waterdrop~~